Prep tomatoes. Cut them into quarters and transfer them to a large pot over medium heat.
Precook tomatoes. Bring to a boil, stirring often. Simmer for 10 minutes until softened.
Run through food mill. Run the softened tomatoes through a food mill to remove skins and seeds.
Simmer sauce. Return the juice to the pot. Simmer over medium-low heat until reduced to desired thickness, 60–90 minutes.
Prep jars and lids. While the sauce reduces, heat clean jars in simmering water. Prepare lids and rings.
Fill jars and add lemon juice. Add 1 tablespoon bottled lemon juice to each pint jar. Ladle hot sauce into jars, leaving ½ inch headspace.
Prep jars. Remove bubbles, wipe rims, and place lids and rings fingertip-tight.
Process in canner. Process jars in boiling water for 35 minutes. Let rest 5 minutes before removing to cool.
Cool. Cool jars undisturbed for 12–24 hours. Check seals, label, and store.